This paper describes an approach for formulation of approximate, generalized field data based mathematical model (FDBM) for the process of PVC pipe manufacturing at some industries. The present work is aimed at establishing mathematical relationship between the responses and inputs at the operation of PVC pipe manufacturing process using single screw extruder. For this purpose various small scale PVC pipes manufacturing industries are visited. The operation of PVC pipe extrusion is studied. The study is focused on an extrusion line starting from its electric motor, extruder hopper, barrel, extruder screw up to the extruder die. First of all the various dependent variables in form of responses and the independent variables in the form of inputs are decided. The categorization of these variables are made in terms of pi terms viz. ?1 ?2 ?3 as independent and ?D1, ?D2, ?D3, ?D4 as dependent variables. Then the field observations are taken and accordingly data collection process is completed. After this step, an approximate, generalized field data based mathematical models are developed. This work presents an approach to check the reliability of models, which is executed by comparing error frequency graphs of various mathematical models formed. After that the influence of the various independent pi terms in the models are studied by analyzing the indices of the various pi terms. Through the technique of sensitivity analysis, the change in the value of a dependent pi term caused due to an introduced change in the value of independent individual pi term is evaluated. The ultimate objective of this work is not merely developing the mathematical models but to find out the best set of independent variables, which will result in maximization or minimization of the objective functions. This is achieved by applying the technique of optimization. Thus the objects of these models are tested to optimize the inputs required for satisfying the various responses. The comparative analysis is made of the outputs of the network with observed data and the data calculated from the mathematical models. This modeling and simulation approach enables entrepreneur of small scale PVC pipes manufacturing industries to get system wide view obtained by deliberately making local changes in their manufacturing system. They can predict its impact on performance of their machines. With the help of the models, one can find a method to improve the productivity of the industry. The results obtained from experiments are also analyzed by the development of different polynomial mathematical models and its related graphs. Recommendations with respect to improvement in the current operation are suggested and future changes are proposed.
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Author Name: Ashish D Vikhar, Dr. J. P. Modak
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Keywords: Field databased mathematical modeling, sensitivity analysis, and optimization